Optical frequency tracking and stabilization based on extra-cavity frequency

ABSTRACT

Embodiments of the invention provides methods and systems for synthesizing optical signals with high frequency stability. Using a set of external optical signal manipulators and control systems, embodiments of the invention enhance the resolution of any frequency reference and thereby alleviates the needs for ultra-high-Q cavities in frequency-stable optical signal synthesis. The invention consequently improves the performance of any optical signal generator by a substantial margin, while maintaining the system complexity and power dissipation at levels comparable to the original systems.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.13/725,563, filed Dec. 21, 2012; which claims priority to U.S.Provisional Patent Application No. 61/700,813, filed on Sep. 13, 2012.The disclosures are hereby incorporated by reference in their entiretyfor all purposes.

BACKGROUND OF THE INVENTION

In analogy to signal synthesis in the electrical domain, optical signalsynthesis technology involves systems and methods for generating opticalsignals with deterministic frequency and amplitude characteristics.Synthesizing optical signals with a high frequency precision andsignal-to-noise ratio (SNR) has enabled numerous novel applications incommunications, sensing and metrology. In one example, low-noise opticaloscillators have allowed existing optical transmission links to attainorders-of-magnitude higher transmission capacity by supporting high-ratecoherent signal transmission. In another example, characteristics ofmultiple chemical species are revealed with unprecedented sensitivityand precision by employing frequency-stabilized optical laser sourcesfor spectroscopic interrogation.

Despite the progress made in optical signal synthesis, there is a needin the art for fiber-based amplifiers with repeatable output pulsecharacteristics independent of the pulse repetition frequency.

SUMMARY OF THE INVENTION

Embodiments of the present invention relate to systems and methods foroptical frequency synthesis and stabilization, and more specifically toa novel high-resolution instantaneous frequency acquisition andfeed-back control system.

Embodiments described herein provide systems for creating opticalsignals carrying amplified replicas of the frequency drift of the inputoptical or electrical oscillators as well as methods of using theseoptical signal to stabilize the frequency of the optical or electricaloscillators. The present invention alleviates the need for high-Qcavities in synthesizing frequency-stable and high-optical signal tonoise ratio (OSNR) optical signals in optical frequency-comb systems.

According to an embodiment of the present invention, a system isprovided. The system includes an input optical signal source operable togenerate a first optical wave and a second optical wave characterized bya first center frequency and a second center frequency, respectively.The first center frequency and the second center frequency are separatedby a frequency spacing. The system also includes an optical frequencymixer coupled to the input optical signal source and operable to inputthe first optical wave and the second optical wave to generate aplurality of third optical waves characterized by respective thirdcenter frequencies separated from each other by the frequency spacing.At least one third center frequency is different from the first centerfrequency and the second center frequency. The system further comprisesa spectral filter coupled to the optical frequency mixer and operable totransmit one of the plurality of third optical waves. The transmittedthird optical wave is characterized by a selected third center frequencythat is different from the first center frequency and the second centerfrequency. Additionally, the system includes an optical frequencyreference coupled to the spectral filter and operable to generate anoutput optical signal characterized by an amplitude that is proportionalto a frequency difference between a reference frequency and the selectedthird center frequency, a photodetector coupled to the optical frequencyreference and operable to convert the output optical signal to anelectrical signal, and a feedback controller coupled to thephotodetector and the input optical signal source. The feedbackcontroller is operable to convert the electrical signal into afrequency-tuning signal and to apply the frequency-tuning signal to theinput optical signal source to adjust the second center frequencythereby stabilizing the second center frequency.

According to another embodiment of the present invention, a method isprovided. The method includes providing, using an input optical signalsource, a first optical wave and a second optical wave characterized bya first center frequency and a second center frequency, respectively.The first center frequency and the second center frequency are separatedby a frequency spacing. The method also includes mixing, via a nonlinearoptical medium, the first optical wave and the second optical wave toprovide an output wave comprising a plurality of third optical wavescharacterized by respective third center frequencies separated from eachother by the frequency spacing. At least one third center frequency isdifferent from the first center frequency and the second centerfrequency. The method further includes spectrally filtering the outputwave to transmit one of the plurality of third optical waves. Thetransmitted third optical wave is characterized by a selected thirdcenter frequency that is different from the first center frequency andthe second center frequency. Additionally, the method includes inputtingthe transmitted third optical wave into an optical frequency referenceto generate an output optical signal characterized by an amplitude thatis proportional to a frequency difference between a reference frequencyand the selected third center frequency, converting the output opticalsignal to an electrical signal, converting the electrical signal to afrequency-tuning signal, and applying the frequency-tuning signal to theinput optical signal source to adjust the second center frequency,thereby stabilizing the second center frequency.

According to an embodiment of the present invention, a method ofcreating optical signals that carry amplified replicas of theinstantaneous frequency drift found in optical or electrical oscillatorsis provided. In one embodiment of the invention, a plurality of opticalsignals are generated by two single-frequency laser sources withdistinct frequencies and are combined to form a single optical signal.The optical signal subsequently undergoes nonlinear interaction withinat least one nonlinear optical medium to generate an opticalfrequency-comb signal, which contains a number of frequency componentsgreater than the number of frequency components at the input of thenonlinear medium. Any of the new frequency tones created in thenonlinear medium contains the amplified frequency drift of the inputlaser sources.

According to another embodiment of the present invention, an opticalsignal is generated by at least one single-frequency laser source and islaunched into at least one electro-optical modulator (EOM). The EOM (orthe set of EOMs) is driven by an electrical signal source and convertsthe input optical signal into an optical frequency-comb in which thenumber of frequency components contained therein is greater than thenumber of frequency components contained in the optical signal at theinput of the EOM. The optical frequency-comb signal may propagatethrough one or multiple nonlinear optical media to further increase thenumber of frequency components.

According to yet another embodiment of the present invention, an opticalsignal is generated by one single-frequency laser source and is launchedinto at least one EOM. The EOM (or the set of EOMs) is driven by anelectrical signal source, which converts the input optical signal intoan optical frequency comb. A set of optical filters then separates thefrequency comb into at least two optical signals, each contains at leastone frequency tone. The optical signals are received by individualoptical circulators, wherein the optical signal is directed to a laserto perform injection locking. The optical signals created by theinjection-locked lasers are subsequently combined and undergo nonlinearinteraction within a nonlinear medium, wherein new optical frequencytones are created.

In another embodiment of the present invention, an optical signal isgenerated by a mode-locked laser source and subsequently undergoesnonlinear interaction within at least one nonlinear optical medium. Thenumber of frequency components of the optical signal at the output ofthe nonlinear optical medium is greater than the number of frequencycomponents of the optical signal generated by the mode-locked lasersource.

In another aspect of the present invention, the amplification offrequency-drift carried by a newly-created frequency component isharnessed to enhance the sensitivity of an optical frequencystabilization system, thereby improving the frequency stability as wellas the OSNR of the optical frequency-comb generated therein. In oneembodiment, at least two frequency components are extracted from theoptical signal generated in the nonlinear optical medium and/or the EOMusing a set of optical filters, and subsequently received by an opticalfrequency reference to convert the frequency drift into thecorresponding intensity fluctuations. The optical frequency referencemay be an optically-transparent enclosure containing at least onechemical species, whereof the absorption lines are aligned with thefrequencies of the received optical signals. Alternatively, the opticalfrequency reference may be an optical resonant cavity, wherein thereceived optical signals can resonate. A set of photodetectors receivesthe transmitted and/or reflected optical signals from the opticalfrequency reference and the photocurrents generated are received by acontroller. Subsequently, the controller generates frequency controlsignals that feed the frequency control mechanisms in the input opticaland/or electrical signal generators, thereby stabilizing the frequencyof the recipient.

In yet another aspect of the present invention, the strict frequencyrelationships between a newly-created frequency component and the inputoptical signals are utilized to enable frequency tuning of the inputoptical signals at a resolution finer than that allowed by theresolution of the optical frequency reference incorporated.

In a further aspect of the present invention, the opticalsignal-to-noise ratio of an optical frequency comb is improved by thepan-spectral frequency stabilization enabled by the invention.

In one embodiment, an optical frequency stabilization system comprises:(a) an input optical signal source operable to provide at least twofrequency tones. The optical frequency tones are equidistance infrequency. The system also includes (b) an optical frequency mixeroperable to create new frequency tones not contained in the inputoptical signal, (c) a bandpass filter, and (d) an optical frequencyreference. The frequency offset of the selected optical signal relativeto the spectral feature of the reference is converted to the amplitudeof the output optical signal. The system further includes (e)photodetectors, wherein the output optical signal from the opticalfrequency reference is converted to an electrical signal, and (f) afeed-back controller, wherein the output electrical signal from thephotodetector is converted to another electrical signal.

In one embodiment, the two optical signals are generated by twoindependent laser sources. The optical signals generated by the lasersources are combined into single optical signal to form the inputoptical signal.

In one embodiment, an optical signal is generated by a combination of anelectro-optical modulator and a single-frequency laser source. Theoptical carrier of the laser source is modulated in an electro-opticalmodulator driven by an electrical signal generator and split into atleast two distinct frequency tones to form the input optical signal.

In one embodiment, an optical signal is generated by a combination of anelectro-optical modulator and single-frequency laser source. The opticalsignal generated by the laser source is modulated in an electro-opticalmodulator driven by an electrical signal generator to form an opticalfrequency comb. At least two frequency tones in the optical frequencycomb are extracted and separated into individual optical signals usingan optical filtering element. Each of the extracted optical signals islaunched into a distinct laser source, wherein the laser source outputis phase-locked to the supplied optical signal by means of injectionlocking. The output optical signals from the phase-locked laser sourcesare combined to form the input signal.

In one embodiment, an optical signal is generated by a passivemode-locked laser. The optical signal generated by the passivemode-locked laser forms the input optical signals.

In one embodiment, an optical signal is generated by an activemode-locked laser. The optical signal generated by the activemode-locked laser forms the input optical signals.

In one embodiment, the mixer contains at least one segment of opticalmedium providing a third-order nonlinear optical response.

In one embodiment, the mixer contains at least one segment of opticalmedium providing a second-order nonlinear optical response.

In one embodiment, the optical reference contains at least one opticalcavity resonator.

In one embodiment, the optical reference contains at least one opticaldiffraction grating.

In another embodiment, the optical reference contains at least onegrating structure inscribed in an optical waveguide.

In one embodiment, the optical signal input to the optical frequencyreference is formed by an absorptive or transmissive response of atleast one chemical species.

In one embodiment, the bandwidth of the absorption or transmission linesin proximity to the frequency of the optical signal input to the opticalfrequency reference is equal to or less than approximately 10 Gigahertz.

In one embodiment, the optical signal input to the optical frequencyreference is combined with a reference optical signal.

In one embodiment, the linewidths of the input optical signals are lessthan or equal to 20 megahertz, defined as the full-width at half-maximumof a spectral line in the self-heterodyne signal with a 1-microseconddelay.

In one embodiment, the feedback controller contains at least oneproportional gain path or derivative gain path or integral gain path, orany combination of proportional, derivative and integral gain paths.

In one embodiment, the feedback controller contains a gain path forwhich the temporal response is matched to the broadening mechanism ofthe input signal laser source.

In another embodiment, a method of operating an optical frequencystabilization system comprises: (a) forming an input optical signal bycombining a first optical signal and a second optical signal, with thefrequencies of the first and second optical signals being distinct, (b)transmitting an input optical signal across the optical frequency mixer,wherein a plurality of new optical frequency tones are generated due tothe nonlinear optical response in the optical frequency mixer, (c)transmitting the optical signal from the optical frequency mixer throughone or more optical filtering elements, wherein new optical frequencytones are extracted to form a frequency-lock optical signal, (d)transmitting the frequency-lock optical signal across an opticalfrequency reference, wherein the frequency position of thefrequency-lock signal is converted to a corresponding amplitude changeof the frequency-lock signal, (e) receiving the output optical signal ofthe optical frequency reference in a photodetector, wherein the measuredoptical power is converted to a corresponding electrical signal, (f)processing the electrical signal from the photodetector in a feedbackcontroller, wherein an electrical frequency-tuning signal is provided byan electronic system according to the electrical signal generated by thephotodetector, and (g) adjusting the frequency of the second opticalsignal according to the frequency-tuning signal, thereby stabilizing thefrequency of the second optical signal.

In a specific embodiment, a method of operating an optical frequencystabilization system comprises: (a) forming an input optical signal bymodulating an optical signal from a laser with an electro-opticalmodulator driven by an electrical signal generator, (b) transmitting aninput optical signal across the optical frequency mixer, wherein aplurality of new optical frequency tones are generated due to thenonlinear optical response in the optical frequency mixer, (c)transmitting the optical signal from the optical frequency mixer throughoptical filtering elements, wherein a new optical frequency tone isextracted to form a frequency-lock optical signal, (d) transmitting thefrequency-lock optical signal across an optical frequency reference,wherein the frequency motion of the frequency-lock signal is convertedto a corresponding amplitude change of the frequency-lock signal, (e)receiving the output optical signal of the optical frequency referencein an photodetector, wherein the measured optical power is converted toa corresponding electrical signal, (f) processing the electrical signalfrom the photodetector in a feedback controller, wherein an electricalfrequency-tuning signal is provided by an electronic system according tothe electrical signal generated by the photodetector, and (g) adjustingthe frequency of the electrical signal generator driving theelectro-optical modulator, thereby stabilizing the frequency of theelectrical signal generator.

In another specific embodiment, a method of operating an opticalfrequency stabilization system comprises: (a) forming an input opticalsignal by combining a first optical signal generated by injectionlocking a laser to a first frequency, and a second optical signalsgenerated by injection locking a laser to a second frequency, whereinthe first and second frequencies are distinct, (b) transmitting an inputoptical signal across the optical frequency mixer, wherein a pluralityof new optical frequency tones are generated due to the nonlinearoptical response in the optical frequency mixer, (c) transmitting theoptical signal from the optical frequency mixer across one or moreoptical filtering elements, wherein a new optical frequency tone isextracted to form a frequency-lock optical signal, (d) transmitting thefrequency-lock optical signal across an optical frequency reference,wherein the frequency motion of the frequency-lock signal is convertedto a corresponding amplitude change of the frequency-lock signal, (e)receiving the output optical signal of the optical frequency referencein an photodetector, wherein the measured optical power is converted toa corresponding electrical signal, (f) processing the electrical signalfrom the photodetector in a feedback controller, wherein an electricalfrequency-tuning signal is provided by an electronic system according tothe electrical signal generated by the photodetector, and (g) adjustingthe frequency of the first optical signal generated according to thefrequency-tuning signal, thereby stabilizing the frequency of the firstoptical signal.

Numerous benefits are achieved by way of the present invention overconventional techniques. For example, embodiments of the presentinvention reduce the residual frequency noise in stabilized opticaland/or electrical frequency sources. Some embodiments provide spectrallinewidth reduction. Additionally, embodiments of the present inventionimprove the signal to noise ratio of optical frequency comb sources.Embodiments of the present invention also enhance the frequencytenability of frequency-stabilized optical sources. As described herein,various embodiments provide practical advantages in multitudeapplications. For example, the invention improves the sensitivity andoperating wavelength range of optical spectroscopy apparatus. As anotherexample, the invention increases the link budget of coherent opticalcommunication systems by reducing the phase noise and amplitude noise ofthe transmitter sources and local oscillators. These and otherembodiments of the invention along with many of its advantages andfeatures are described in more detail in conjunction with the text belowand attached figures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates the generation of an optical frequency comb in anoptical frequency mixer, according to an embodiment of the invention;

FIG. 2 illustrates the frequency-drift scaling phenomenon in an opticalfrequency comb generation process, according to an embodiment of theinvention;

FIG. 3A illustrates an optical frequency stabilization system thatincorporates an optical frequency mixer according to an embodiment ofthe invention;

FIG. 3B illustrates an optical frequency stabilization system thatincorporates an optical frequency mixer and a feedback signal accordingto an embodiment of the present invention;

FIG. 4 shows experimental results of the spectral lineshapes of a seedlaser according to various embodiments of the invention;

FIG. 5 shows experimental results of the spectral linewidths of a seedlaser according to various embodiments of the invention; the inset showsexperimental results of the spectral lineshapes of the seed laseraccording to various embodiments of the invention;

FIG. 6A illustrates tuning in frequency-stabilized laser systems enabledby extra-cavity frequency scaling process including tuning with respectto a single reference point by locking to the adjacent (N+1) tone orderaccording to an embodiment of the present invention;

FIG. 6B illustrates tuning in frequency-stabilized laser systems enabledby extra-cavity frequency scaling process including tuning with respectto a periodic reference by locking to the adjacent spectral markeraccording to an embodiment of the present invention;

FIG. 6C illustrates tuning in frequency-stabilized laser systems enabledby extra-cavity frequency scaling process including fine frequencytuning by locking to the nearest vernier step according to an embodimentof the present invention;

FIG. 7 shows frequency spectra of the optical frequency tones with andwithout frequency stabilization system engaged, according to embodimentsof the invention;

FIG. 8 is a simplified block diagram of a frequency stabilization systemaccording to an embodiment of the invention;

FIG. 9 is a simplified schematic diagram of a frequency stabilizationsystem according to another embodiment of the invention;

FIG. 10 is a simplified flowchart illustrating a method of frequencystabilizing an optical source according to an embodiment of the presentinvention; and

FIGS. 11A and 11B illustrate alternative optical sources according toembodiments of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Embodiments of the invention provide methods and systems forsynthesizing optical signals with the frequency stability better thanthe level allowed by the optical cavities incorporated in the opticalsignal generators. Using a set of external optical signal manipulatorsand control systems, the invention enhances the resolution of anyfrequency reference and thereby alleviates the needs for ultra-high-Qcavities in frequency-stable optical signal synthesis. The inventionconsequently improves the performance of any optical signal generator bya substantial margin, while maintaining the system complexity and powerdissipation at levels comparable to the original systems.

While conventional applications are primarily fulfilled bysingle-frequency optical signals, emerging applications are demanding anew form of optical radiation that possesses multiple phase-lockedfrequency tones, namely optical frequency combs. The instantaneousfrequencies of the component tones in an optical frequency comb isdefined by their frequency spacing Δf and the carrier-envelope offsetfrequency f_(CEO). Consequently, the frequency precision of anindividual frequency tone in an optical frequency comb signal isdirectly related to the stability of the Δf and f_(CEO). Opticalfrequency combs with highly-stable frequency spacing andcarrier-envelope offset frequency have enabled a number of newexplorations. For instance, certain characteristics of a chemicalspecies can be known with orders-of-magnitude higher precision bymeasuring the transition frequency of the energetically-excited speciesin the optical domain. In another example, the utility offrequency-stable optical frequency combs reduces the system complexityof an optical communication link yet simultaneously attains higherperformance.

Optical signal generation couples with a certain form of an opticallyresonant cavity in order to accumulate an optical signal in a coherentmanner, thereby defining the signal's frequency and amplitudecharacteristics. The frequency and amplitude stability of the generatedoptical signal are primarily determined by the quality of the opticalcavity, measured in terms of a Q-factor. A higher Q-factor cavitypossesses a finer resonance signature in the frequency domain, whichleads to a smaller amount of frequency drift in the generated opticalsignal. Simultaneously, the narrow spectral pass-band of a high Q-factorcavity provides better rejection to the non-resonant portion of theoptical signal, thereby resulting in lower amplitude fluctuations in thegenerated optical signal due to interference between the resonant andnon-resonant (i.e., noise) components.

Although contemporary art in optical surface processing and materialsengineering allows one to construct a cavity with an extremely highQ-factor, the quality and characteristics of a high-Q cavity in terms offrequency resolution, spacing and spectral positions of the cavity'sresonant modes are seldom repeatable in manufactured devices,consequently, rendering mass-production with guaranteed performancedifficult if not unrealistic. Furthermore, the resonance frequency of ahigh-Q cavity is inherently susceptible to drift due to mechanicaland/or thermal perturbation. Consequently, operating with a high-Qcavity typically requires a sophisticated environmental isolationplatform in order to attain the desired performance. The complicationassociated with the complexity of environmental isolation becomesoppressive in scenarios in which a sizable number of high-qualityoptical signals are needed—stabilizing a large number of opticalcavities not only requires substantial excess real estate, but alsodrives the power consumption and thermal dissipation to an unmanageablelevel.

In one embodiment of the present invention, an optical frequencystabilization system is provided, which enables frequency stabilizationas well as tracking to a precision not permitted by conventional means.FIG. 1 illustrates the generation of an optical frequency comb in anoptical frequency mixer, according to an embodiment of the invention. Inthe simplified system depicted in FIG. 1, the input to the systeminvolves an optical signal 110 containing two distinct frequency tones,each generated by a separate laser. The frequency of the first frequencytone is denoted as f₀ whereas the second frequency tone is separatedfrom the first tone by a frequency offset Δf, thereby occupying thefrequency f₁=f₀+Δf. Upon propagation in the optical frequency mixer 120comprising a combination of nonlinear optical media, the nonlinearoptical interaction between the first and second frequency tonesgenerates an optical frequency comb 130 containing a plurality of newfrequency tones. The frequencies of the new tones follow therelationship below, owing to the law of conservation of energy in thenonlinear optical process:f _(n) =f ₀ +n×Δf  (1)where the index n indicates the spectral position relative to the firstfrequency tone, which is also known as the order of the tone. In thepresence of frequency drift in the first and second frequency tones, thefrequency of the new tones will inherit the drift carried by the inputtones. The frequency relationship conveyed in Eq. (1) is subsequentlymodified as follow:(f ₀+δ₀)+n×[(f ₁+δ₁)−(f ₀+δ₀)]=f ₀ +n×Δf+[n×(δ₁−δ₀)+δ₀ ]=f_(n)+δ_(n)  (2)where δ₀ and δ₁ are the instantaneous frequency deviation of the firstand second frequency tones, respectively. The relationship in Eq. (2)demonstrates an important property in regards to the frequencycharacteristics of a new tone—the frequency drift of the new tone is anamplified replica of the deviations introduced by the first and secondtones.

The present invention subsequently harnesses the frequency-driftamplification effect to enhance the resolution of any existing frequencymeasurement system, thereby improving the accuracy of frequency locking.In one example, the first optical signal is supplied by afixed-frequency laser source, whereas the second optical signal isgenerated by a tunable laser source. The tunable laser source, owing tothe environmental perturbation to the reconfigurable optical cavityincorporated therein, generates the second optical signal, whichexhibits an appreciable amount of frequency drift. In contrast, thenon-tunable optical cavity in the fixed-frequency laser source isinherently less sensitive to external perturbation, thus inferring thatthe extent of frequency drift conveyed by the first optical signal (δ₀)is substantially lower than that of the second optical signal (δ₁).

FIG. 2 illustrates the frequency-drift scaling phenomenon in an opticalfrequency comb generation process, according to an embodiment of theinvention. The frequency deviations carried by the new frequency tonesis therefore dominated by the contribution from the second opticalsignal, as illustrated in FIG. 2:δ_(n) =n×(δ₁−δ₀)+δ₀ ≈n×δ ₁  (3)

Consequently, the amplified frequency deviation carried by the newfrequency tones provides an improvement to the measurement of thefrequency drift of the tunable laser source, overcoming the classicallimit due to the detection noise and/or the ambiguity in the opticalfrequency reference.

FIG. 3A illustrates an optical frequency stabilization system thatincorporates an optical frequency mixer according to an embodiment ofthe invention. Referring to FIG. 3A, the N^(th)-order tone generated inan optical frequency mixer 310 fed by a first optical source 305 and asecond optical source 307 is extracted in the frequency detector 315,and subsequently received by the optical frequency reference 320. In anembodiment, the first optical source 305 and the second optical source307 form an input optical signal source that is operable to generate afirst optical wave and a second optical wave characterized by a firstcenter frequency (f₀ associated with the first optical source) and asecond center frequency (f₁ associated with the second optical source),respectively. The first center frequency and the second center frequencyare separated by a frequency spacing (f₁-f₀).

The system also includes an optical frequency mixer 310 coupled to theinput optical signal source and operable to input the first optical waveand the second optical wave to generate a plurality of third opticalwaves characterized by respective third center frequencies separatedfrom each other by the frequency spacing. At least one third centerfrequency is different from the first center frequency and the secondcenter frequency. The optical frequency mixer is also utilized in otherembodiments of the present invention.

FIG. 3B illustrates an optical frequency stabilization system thatincorporates an optical frequency mixer 360 and a feedback signalaccording to an embodiment of the present invention. Referring to FIG.3B, the frequency detector 365 converts the frequency drift of theN^(th)-order tone relative to the spectral feature of the opticalfrequency reference 370, and produces a feedback signal 361 thatcontrols the instantaneous frequency of the second optical source 357(f₁). The frequency ambiguity (δ_(ref)) of the frequency reference 370is reduced to δ_(ref)/N in the frequency of the stabilized secondoptical source 357, when the first optical source 355 carries aninsignificant amount of frequency drift compared to that of the secondoptical source 357 (δ) and the frequency ambiguity of the opticalfrequency reference 370 (δ_(ref)). For example, assuming the opticalfrequency reference provides an absolute frequency accuracy of δ_(ref),stabilizing the frequency of the second optical signal (e.g., a tunablelaser source) using the N^(th)-order frequency tone (FIG. 3A) willresult in a frequency accuracy approaching δ_(ref)/N (FIG. 3B), thusinferring an improvement in frequency-locking accuracy by a factor of Ncompared to the direct frequency stabilization using the given opticalfrequency reference.

Benefits of the invention in a practical laser system are demonstratedin FIG. 4 and FIG. 5. FIG. 4 shows experimental results of the spectrallineshapes of a seed laser according to various embodiments of thepresent invention. The extent of frequency drift, described by thehalf-width at −3 dB of the self-heterodyne spectrum of the secondoptical source, was reduced from 1.2 MHz to 4.4 kHz when the disclosedsystem was engaged. FIG. 5 shows experimental results of the spectrallinewidths of a seed laser according to various embodiments of theinvention. The −3 dB half-width of the self-heterodyne spectrum of thesecond optical source decreased to 4.4 kHz when the 5^(th)-order tonewas selected for frequency measurement, versus 13.6 kHz when the opticalsource was directly stabilized against the same frequency reference.With the frequency stabilization system engaged, the half-power (−3 dB)spectral width of the second optical frequency tone (f₁) measured by theself-heterodyning method was reduced from 1.2 MHz to 4.4 kHz (FIG. 4).When compared to the conventional configuration, in which the opticalsource is directly stabilized against the optical frequency reference,the mixer-aided stabilization system described herein improves thefrequency stability by more than 300%, when the 5^(th)-order tone wasused for referencing (FIG. 5). Indeed, the stability improved when afrequency tone of higher order was locked to the optical frequencyreference, as depicted by the trend of decreasing spectral width in FIG.5.

In addition to frequency stabilization, embodiments of the presentinvention also provide a new mechanism for a first optical signal totrack the frequency motion of a second optical signal that has adifferent frequency from the first optical signal. Assuming the opticalfrequency reference can provide a perfect frequency accuracy (i.e.,δ_(ref)=0), restricting the frequency of the N^(th)-order tone to thefrequency reference will imply N×(δ₁−δ₀)+δ₀=0. With a high-performanceoptical frequency mixer for which N>>1 is possible, the differencebetween the frequency deviation of the first and second optical signalswill approach zero (with a residue equal to δ₀/N), meaning that thefrequency of the second optical signal tracks that of the first opticalsignal. Even in the presence of the reference ambiguity (i.e.(δ_(ref)>0), the frequency of the second optical signal will continue totrack the first optical signal's frequency drift, only with a diminishedpenalty given by δ_(ref)/N.

The mode of frequency tracking provided by embodiments of the inventionovercomes the frequency separation limit found in a conventionalfrequency tracking system. Conventional tracking systems require thesecond optical signal to generate a new tone with its frequency matchingthe frequency of the first optical signal. Typical means for new tonegeneration involve electro-optical modulation driven by an electricalsignal source. The bandwidth limit in the electrical signal source, aswell as in the electro-optical modulator, consequently constrains thefrequency separation between the first and the second optical signal towithin tens of gigahertz. In sharp contrast, the methods and systemsprovided by embodiments of the present invention allow at least ahundred times wider separation while maintaining tracking. The newregime of frequency tracking is likely to be found useful inmulti-wavelength optical communication systems, in which the frequencyof the spectrally-diverse channels should follow a pilot frequency tonein order to maintain link interoperability across the entire network.The new frequency tracking function will also be useful in sensing andranging applications, wherein a plurality of distinct frequency tonesare allowed to scan across a spectral range in perfect unison forproviding new sensing/imaging modality as well as enhancing the systemsensitivity.

Further to the aforementioned functionalities, the frequencystabilization system provided by embodiments of the invention entails anew mode of frequency tuning not permitted by any conventional means. Ina direct frequency-locking system, tuning of the emission frequency mustbe accomplished through reconfiguration of the frequency reference.However, swift reconfiguration and high stability cannot be achievedsimultaneously by the same frequency reference, since a stable referencemust be resistive to any perturbation to its configuration, regardlessto the nature of perturbation. Even though tunability needs can beaddressed by incorporating multiple frequency references or a periodicspectral reference (e.g., Fabry-Perot etalon), tuning is allowed onlyamong a sparse set of spectral positions defined by the reference. Incontrast, the comb of frequency-locked optical tones created in theoptical frequency mixer can release the emission frequency anchor to thespectral reference while maintaining frequency stability.

FIG. 6A illustrates tuning in frequency-stabilized laser systems enabledby extra-cavity frequency scaling process including tuning with respectto a single reference point by locking to the adjacent (N+1) tone orderaccording to an embodiment of the present invention. With a frequencyreference having a single spectral marker R(f), frequency tuning of theseed is accomplished by locking an arbitrary mixing product to thefrequency reference.

FIG. 6B illustrates tuning in frequency-stabilized laser systems enabledby extra-cavity frequency scaling process including tuning with respectto a periodic reference by locking to the adjacent spectral markeraccording to an embodiment of the present invention. In the case inwhich a periodic frequency reference R(f) is deployed, the invention canimprove the seed tuning resolution from the frequency spacing S ofreference point to S/N by locking the N^(th)-order tone to the referencefrequency grid.

FIG. 6C illustrates tuning in frequency-stabilized laser systems enabledby extra-cavity frequency scaling process including fine frequencytuning by locking to the nearest vernier step according to an embodimentof the present invention. This embodiment achieves further granularityenhancement when the frequency grids of the reference points and opticaltones constitute a vernier scale (i.e. the frequency separations areco-prime), in which an adjacent tone (e.g. the (N−1)^(th)-order) islocked to its nearest spectral reference to complete a seed frequencyjump.

The present invention is also applicable to improving the performance ofan optical frequency comb generation system. Broadband optical frequencycomb sources typically incorporate a nonlinear optical medium to expandthe spectral span of the output optical frequency comb. While thenonlinear optical medium enables new tone generation by a cascade ofnonlinear interactions between the existing frequency tones, theinteraction will also transfer the frequency drift in the existing tonesto the new tones, and thereby amplify the drift in the tone frequencyspacing by the same mechanism transcribed by Eq. (2). The increase offrequency drifts in the newly generated, outlying frequency tones notonly severs the coherence, but also decreases the opticalsignal-to-noise ratio of the entire frequency comb. The presentinvention quenches the uncontrolled coherence-fading in anonlinearly-broadened optical frequency comb by stabilizing the outmostfrequency tones to a narrow frequency reference through stabilizing thefrequency separation of the input optical frequency comb. Since thefrequency of all the tones are defined upon the frequency separation,the frequency stabilization will result in an improvement of tonecoherence across the entire comb spectrum.

FIG. 7 shows frequency spectra of the optical frequency tones with andwithout frequency stabilization system engaged, according to embodimentsof the invention. As illustrated in FIG. 7, the spectra of an opticalfrequency tone in an optical frequency comb before and after frequencyseparation stabilization are shown. Not only is the spectral width ofthe frequency tone reduced, but the optical signal-to-noise ratios, aswell as the generation efficiencies, are improved simultaneously, owingto the suppression of frequency-noise.

Embodiments of the present invention enable a variety of opticalfrequency measurement and feedback systems to stabilize the frequency ofthe input optical signals. The frequency stabilization system canincorporate a set of optical filters to extract a new frequency tone notpresent in the input optical signal. The new optical signal formed bythe extracted frequency tone is subsequently received by an opticalfrequency reference, wherein the amount of frequency deviation relativeto the target frequency of the optical frequency reference is measured.The frequency deviation measurement is performed in concert with adetection system.

FIG. 8 is a simplified block diagram of a frequency stabilization systemaccording to an embodiment of the invention. In the example shown inFIG. 8, the detection system resembles a Pound-Drever-Hall (PDH)frequency-demodulation system, wherein an electro-optical phasemodulator 820 placed at the input of the optical frequency reference 840operates with a set of photodetector 850, optical circulator 830,electrical mixer 854 and filters 860 to derive an electrical signal(Frequency Feedback Signal). The phase modulator 820 imprints at leasttwo additional frequency components on the extracted optical frequencytone, wherein the new components are separated from the extracted toneby the frequency of the driving electrical signal source 852, denoted asΩ hereinafter. The drift of frequency from the center of the spectralfeature of the optical frequency reference 840 will result in acorresponding change in the phase of the photo-current generated by thephotodetector 850 at the frequency Ω. The electrical mixer 854demodulates the phase at frequency Ω carried by the photo-current,resulting in an electrical signal approximately proportional to thefrequency drift of the extracted optical tone relative to the opticalfrequency reference.

The system includes an input optical signal source operable to generatea first optical wave and a second optical wave characterized by a firstcenter frequency and a second center frequency, respectively, the firstcenter frequency and the second center frequency being separated by afrequency spacing. As illustrated in FIG. 8, the input optical signalsource includes a first laser source 805 and a second laser source 807operable to generate the first optical wave (frequency f₀) and thesecond optical wave (frequency f₁), respectively. The first laser sourceand the second laser source are independent from each other in thisembodiment. In an embodiment, the input signal source includes a passivemode-locked laser or an active mode-locked laser.

In one implementation, the spectral linewidth of the first optical waveis not greater than about 20 megahertz. In these embodiments, thespectral linewidth of the first optical wave is defined by thefull-width at half-maximum of a spectral line in the self-heterodynespectrum with a 1-microsecond delay.

The system also includes an optical frequency mixer 810 coupled to theinput optical signal source and operable to input the first optical waveand the second optical wave to generate a plurality of third opticalwaves characterized by respective third center frequencies separatedfrom each other by the frequency spacing. At least one third centerfrequency is different from the first center frequency and the secondcenter frequency. As an example, the optical frequency mixer can includea nonlinear optical medium such as an optical fiber, fiber opticwaveguides, lithium niobate waveguides, or silicon waveguides,chalcogenide waveguides, or the like. At least one segment of thenonlinear optical medium can be characterized by a third-order nonlinearoptical response. Alternatively, the nonlinear optical medium can haveat least one segment characterized by a second-order nonlinear opticalresponse.

The system further includes a spectral filter (i.e., optical band passfilter 815) coupled to the optical frequency mixer 810 and operable totransmit one of the plurality of third optical waves. In the illustratedembodiment, the third optical wave is at frequency f₀+NΔf. Thetransmitted third optical wave is characterized by a selected thirdcenter frequency that is different from the first center frequency andthe second center frequency.

Moreover, the system includes an optical frequency reference 840 coupledto the spectral filter (i.e., the optical band pass filter) and operableto generate an output optical signal characterized by an amplitude thatis proportional to a frequency difference between a reference frequencyand the selected third center frequency. The optical frequency referencecan be provided in one of several forms, including an optical cavityresonator, a diffraction-based device including at least one opticaldiffraction grating, or the like. As an example, the at least oneoptical diffraction grating can be embedded in an optical fiber orprovided as a discreet component. In some implementations, the referencefrequency is a characteristic frequency of an absorption or transmissionresponse of a chemical species, for example, acetylene, cesium, hydrogencyanide, or the like. In a particular embodiment, the absorption ortransmission response of the chemical species is characterized by abandwidth of less than about 10 GHz.

A photodetector 850 is coupled to the optical frequency reference 840and operable to convert the output optical signal to an electricalsignal. A feedback controller 860 is coupled to the photodetector andthe input optical signal source. As illustrated in FIG. 8, the feedbackcontroller 860 is operable to convert the electrical signal into afrequency-tuning signal and to apply the frequency-tuning signal to theinput optical signal source. The frequency feedback signal is applied tothe second optical source 807 in FIG. 8 to adjust the second centerfrequency and thereby stabilizing the second center frequency.

The feedback controller can take several forms including use of aproportional gain path, a derivative gain path, an integral gain path,or a combination thereof. In a particular embodiment, the feedbackcontroller includes a gain path characterized by a temporal responsethat is matched to a spectral linewidth broadening mechanism of theinput optical signal source. As an example, a proportional integralderivative (PID) controller or other suitable controllers.

Although the input optical signal source illustrated in FIG. 8 includesfirst laser source 805 and second laser source 807 operable to generatethe first optical wave (frequency f₀) and the second optical wave(frequency f₁), respectively, the invention is not limited to thisparticular input optical source. FIGS. 11A and 11B illustratealternative optical sources that can be used in place of or in additionto lasers 805 and 807 in the input optical source.

Referring to FIG. 11A, input optical source 1110 includes a seed lasersource 1115 operable to generate a seed optical wave characterized by aseed center frequency and an optical modulator 1120 driven by signalsource 1117 and operable to transform the seed optical wave into thefirst optical wave and the second optical wave, illustrated at frequencyf₀ and frequency f₀+Δf, respectively. As an example, optical modulator1120 can be an electro-optical modulator, for example, either anamplitude modulator or a phase modulator.

Referring to FIG. 11B, in another alternative embodiment, the inputsignal source 1150 includes a seed laser source 1155 operable togenerate a seed optical wave characterized by a seed center frequency.The input optical source 1150 also includes an optical modulator 1160coupled to the seed laser source and operable to transform the seedoptical wave into a first intermediate optical wave and the secondintermediate optical wave characterized by the first center frequencyand the second center frequency, respectively. Additionally, the inputoptical source 1150 includes a first slave source 1170 and a secondslave source 1175 coupled to the optical modulator 1160 and operable toemit the first optical wave and the second optical wave, respectively.Injection locking using the first intermediate optical wave and thesecond intermediate optical wave, respectively is performed inconjunction with optical splitter S1 and optical coupler W2 as well asoptical circulators 1180 and 1182.

Referring once again to FIG. 11A, in some embodiments, the input opticalsignal source includes not only a seed laser source 1115 operable togenerate a seed optical wave characterized by a seed center frequencyand an optical modulator 1120 coupled to the seed laser source andoperable to transform the seed optical wave into a plurality of inputoptical waves including the first optical wave and the second opticalwave, but also includes a spectral filter 1130 coupled to the opticalmodulator 1120 and operable to transmit the first optical wave and thesecond optical wave to the optical frequency mixer 810.

FIG. 9 is a simplified schematic diagram of a frequency stabilizationsystem according to another embodiment of the invention. In the exampleshown in FIG. 9, the detection system comprises a photodetector 945/944that is configured to receive either the transmitted optical signal orthe reflected optical signal (through an optical circulator) from theoptical frequency reference 940/942. The extracted optical frequencytone is set to align its mean frequency to one of the edges of thespectral feature conveyed by the optical frequency reference. Thefrequency drift of the extracted optical signal is consequentlyconverted to the power of the transmitted (or reflected) optical signalfrom the optical frequency reference. Photodetection of the transmitted(or reflected) optical signal thus results in an electrical signalproportional to the frequency offset relative to the mean frequency.Regardless to the implementation of the frequency detection system, theelectrical signal derived from the detection system in the opticalfrequency reference conveys the information regarding to theinstantaneous deviation of the frequency separation in the input opticalfrequency comb. The electrical signal is subsequently received by afeedback controller, wherein a corresponding frequency correction signalis derived. While various implementations of the feedback controllerexist, the basic form of the controller comprises a combination offunctional blocks providing gain directly to the input electrical signal(denoted as proportional gain), to the time-integral of the input signal(integral gain), or to the time-derivative of the input signal(derivative gain). The feedback controller combines the contribution ofall the gain blocks, and may add in any addition external signals asappropriate, to form a frequency correction signal. The frequencycorrection signal is then received by at least one of the input opticalsignal source, or the electrical signal source responsible for definingthe comb frequency separation, in order to correct the frequency driftdetected by the frequency stabilization system.

FIG. 10 is a simplified flowchart illustrating a method of frequencystabilizing an optical source according to an embodiment of the presentinvention. The method 1000 includes providing, using an input opticalsignal source, a first optical wave and a second optical wavecharacterized by a first center frequency and a second center frequency,respectively (1010). The first center frequency and the second centerfrequency are separated by a frequency spacing.

In an embodiment, providing the first optical wave and the secondoptical wave includes providing a seed optical signal and modulating theseed optical signal to provide the first optical wave and the secondoptical wave. In another embodiment, providing the first optical waveand a second optical wave includes providing a seed optical signal,modulating the seed optical signal to provide the first intermediateoptical wave and the second intermediate optical wave characterized bythe first center frequency and the second center frequency,respectively, and injection locking a first slave laser and a secondlaser, using the first intermediate optical wave and the secondintermediate optical wave, respectively, to generate the first opticalwave and the second optical wave. In yet another embodiment, providingthe first optical wave and the second optical wave includes providing aseed optical signal, modulating the seed optical signal to provide aplurality of input optical waves including the first optical wave andthe second optical wave, and spectrally filtering the plurality of inputoptical waves to transmit the first optical wave and the second opticalwave.

The method also includes mixing, via a nonlinear optical medium, thefirst optical wave and the second optical wave to provide an output wavecomprising a plurality of third optical waves characterized byrespective third center frequencies separated from each other by thefrequency spacing (1012). At least one third center frequency isdifferent from the first center frequency and the second centerfrequency.

The method further includes spectrally filtering the output wave totransmit one of the plurality of third optical waves (1014). Thetransmitted third optical wave is characterized by a selected thirdcenter frequency that is different from the first center frequency andthe second center frequency. Additionally, the method includes inputtingthe transmitted third optical wave into an optical frequency referenceto generate an output optical signal characterized by an amplitude thatis proportional to a frequency difference between a reference frequencyand the selected third center frequency (1016).

The method also includes converting the output optical signal to anelectrical signal (1018), converting the electrical signal to afrequency-tuning signal (1020), and applying the frequency-tuning signalto the input optical signal source to adjust the second centerfrequency, thereby stabilizing the second center frequency (1022).

It should be appreciated that the specific steps illustrated in FIG. 10provide a particular method of providing a frequency stabilized signalaccording to an embodiment of the present invention. Other sequences ofsteps may also be performed according to alternative embodiments. Forexample, alternative embodiments of the present invention may performthe steps outlined above in a different order. Moreover, the individualsteps illustrated in FIG. 10 may include multiple sub-steps that may beperformed in various sequences as appropriate to the individual step.Furthermore, additional steps may be added or removed depending on theparticular applications. One of ordinary skill in the art wouldrecognize many variations, modifications, and alternatives.

It is also understood that the examples and embodiments described hereinare for illustrative purposes only and that various modifications orchanges in light thereof will be suggested to persons skilled in the artand are to be included within the spirit and purview of this applicationand scope of the appended claims.

What is claimed is:
 1. A system comprising: an input optical signalsource operable to generate a first optical wave characterized by afirst center frequency and a second optical wave characterized by asecond center frequency, the first center frequency and the secondcenter frequency being separated by a frequency spacing; an opticalfrequency mixer coupled to the input optical signal source and operableto generate a plurality of third optical waves characterized byrespective third center frequencies separated from each other by thefrequency spacing; an electro-optic phase modulator coupled to theoptical frequency mixer; an electrical signal generator coupled to theelectro-optic phase modulator and operable to provide an electricaldrive signal; an optical frequency reference coupled to theelectro-optic phase modulator; and a feedback loop including aphotodetector having an electrical output and operable to couple theoptical frequency reference to the input optical source, wherein thefeedback loop includes an electrical mixer operable to combine theelectrical drive signal and the electrical output of the photodiode. 2.The system of claim 1 further comprising an optical circulator coupledto the electro-optic phase modulator and the optical frequencyreference.
 3. The system of claim 2 wherein the photodetector is coupledto the optical circulator.
 4. The system of claim 1 wherein the opticalfrequency reference is operable to generate an output optical signalcharacterized by an amplitude that is proportional to a frequencydifference between a reference frequency and a third center frequency.5. The system of claim 1 further comprising a spectral filter coupled tothe optical frequency mixer and operable to transmit one of theplurality of third optical waves.
 6. The system of claim 5 wherein thetransmitted third optical wave is characterized by a third centerfrequency that is different from the first center frequency and thesecond center frequency.
 7. The system of claim 1 wherein the inputoptical signal source comprises a first laser source and a second laseroperable to generate the first optical wave and the second optical wave,respectively, wherein the first laser source and the second laser sourceare independent from each other.
 8. The system of claim 1 wherein theinput optical signal source comprises: a seed laser source operable togenerate a seed optical wave characterized by a seed center frequency;and an optical modulator operable to transform the seed optical waveinto the first optical wave and the second optical wave.
 9. The systemof claim 8 wherein the optical modulator comprises an electro-opticalmodulator.
 10. The system of claim 8 wherein the optical modulatorcomprises an amplitude modulator or a phase modulator.
 11. The system ofclaim 1 wherein the optical frequency mixer comprises a nonlinearoptical medium comprising at least one segment characterized by athird-order nonlinear optical response.
 12. The system of claim 1wherein the optical frequency mixer comprises a nonlinear optical mediumcomprising at least one segment characterized by a second-ordernonlinear optical response.
 13. The system of claim 1 wherein theoptical frequency reference comprises an optical cavity resonator.
 14. Amethod comprising: providing, using an input optical signal source, afirst optical wave characterized by a first center frequency and asecond optical wave characterized by a second center frequency, thefirst center frequency and the second center frequency being separatedby a frequency spacing; mixing the first optical wave and the secondoptical wave in an optical frequency mixer coupled to the input opticalsignal source; generating a plurality of third optical wavescharacterized by respective third center frequencies separated from eachother by the frequency spacing; inputting at least one of the pluralityof third optical waves into an electro-optic phase modulator driven byan electrical drive signal; inputting at least one of the plurality ofmodulated third optical waves into an optical frequency reference,wherein the at least one of the plurality of modulated third opticalwaves is characterized by a third center frequency; generating an outputoptical signal; converting the output optical signal to an electricalsignal; mixing the electrical drive signal and the electrical signal;and adjusting the second center frequency.
 15. The method of claim 14further comprising: converting the mixed electrical drive signal and theelectrical signal to a frequency-tuning signal; and applying thefrequency-tuning signal to the input optical signal source to adjust thesecond center frequency.
 16. The method of claim 14 wherein the outputoptical signal is characterized by an amplitude that is proportional toa frequency difference between a reference frequency and the thirdcenter frequency.
 17. The method of claim 14 further comprisingspectrally filtering the plurality of third optical waves to pass the atleast one of the plurality of third optical waves.
 18. The method ofclaim 17 wherein the at least one of the plurality of third opticalwaves is characterized by a selected third center frequency that isdifferent from the first center frequency and the second centerfrequency.
 19. The method of claim 14 wherein providing the firstoptical wave and a second optical wave comprises: providing a seedoptical signal; modulating the seed optical signal to provide the firstintermediate optical wave and the second intermediate optical wavecharacterized by the first center frequency and the second centerfrequency, respectively; and injection locking a first slave laser and asecond laser, using the first intermediate optical wave and the secondintermediate optical wave, respectively, to generate the first opticalwave and the second optical wave.
 20. The method of claim 14 whereinproviding the first optical wave and the second optical wave comprises:providing a seed optical signal; modulating the seed optical signal toprovide a plurality of input optical waves including the first opticalwave and the second optical wave; and spectrally filtering the pluralityof input optical waves to transmit the first optical wave and the secondoptical wave.